Question

(27/5z+31/3)•3/5=1/6z+61/2​

Answer 1

Ответ:

Пошаговое объяснение:

(27/5z+31/3)*3/5=1/6z+61/2;

27/5z*3/5+31/3*3/5=1/6z+61/2;

27*3/5*5z+31*3/3*5=1/6z+61/2;

81/25z+31/5=1/6z+61/2;

81/25z+31/5-1/6z=61/2;

461/150z+31/5=61/2;

461/150z=61/2-31/5;

461/150z=305/10-62/10;

461/150z=305-62/10;

461/150z=243/10;

z=243/10*150/461;

z=243*150/10*461;

z=36450/4610;

z=3645/461

Надеюсь правильно)

Answer 2

To solve the equation $\frac{27}{5z} + \frac{31}{3} \cdot \frac{3}{5} = \frac{1}{6z} + \frac{61}{2}$, we can follow these steps:

1. Simplify the equation on both sides.

Starting with the left side:

$\frac{27}{5z} + \frac{31}{3} \cdot \frac{3}{5} = \frac{27}{5z} + \frac{31}{5}$

And on the right side, we can simplify $\frac{1}{6z}$ as follows:

$\frac{1}{6z} = \frac{1}{6} \cdot \frac{1}{z} = \frac{1}{6z}$

So the equation becomes:

$\frac{27}{5z} + \frac{31}{5} = \frac{1}{6z} + \frac{61}{2}$

2. To get rid of the fractions, we can find a common denominator, which in this case is 30z:

Multiply both sides by $30z$:

$(30z) \cdot \left(\frac{27}{5z} + \frac{31}{5}\right) = (30z) \cdot \left(\frac{1}{6z} + \frac{61}{2}\right)$

Now, we have:

$\frac{30z \cdot 27}{5z} + \frac{30z \cdot 31}{5} = \frac{30z \cdot 1}{6z} + \frac{30z \cdot 61}{2}$

3. Simplify the equation further:

On the left side, the $z$ in the numerator and denominator cancel out:

$\frac{30 \cdot 27}{5} + \frac{30 \cdot 31}{5} = \frac{30}{6} + \frac{30 \cdot 61}{2}$

4. Continue simplifying:

$\frac{30 \cdot 27}{5} + \frac{30 \cdot 31}{5} = 5 + 30 \cdot 61$

5. Calculate the values:

$\frac{810}{5} + \frac{930}{5} = 5 + 1830$

Now, we have:

$\frac{810 + 930}{5} = 5 + 1830$

$\frac{1740}{5} = 5 + 1830$

6. Simplify the left side further:

$\frac{1740}{5} = 1835$

7. Solve for $z$:

To isolate $z$, multiply both sides of the equation by $\frac{5}{1740}$:

$z = \frac{5}{1740} \cdot 1835$

Now, calculate $z$:

$z = \frac{5}{1740} \cdot 1835 \approx 5.2759$